The primary objectives of this single institution trial are to determine the toxicity, tumor response, and survival of patients with AIDS-related systemic lymphoma who are given combination chemotherapy with Doxil, cyclophosphamide, vincristine and prednisone (Doxil-CVP). Other objectives are to evaluate the effects of treatment with Doxil-CVP on plasma viral RNA levels, CD4+ counts and the incidences and types of opportunistic infection in patients with AIDS-related lymphoma. CSF penetration of Doxil in patients receiving intrathecal chemotherapy for prophylaxis of the CNS will be determined.